We describe a new method for generating overlapping fragments for use in DNA sequencing. This procedure is unique because no exonucleases or endonucleases are required. This method improves upon other procedures in several ways. No timed enzymatic reaction is necessary to produce the deletions. The deletions are identified by blue/white screening. The preparation of large amounts of DNA is unnecessary. In addition we describe the constrution of a new DNA vector in which the efficiency of isolating clones with deletions in a DNA fragment will approach 100%. Improvement of DNA sequencing has important commercial applications. Sequencing of genes would be more rapid. Large- scale sequencing projects would become more cost effective, especially when our vector is integrated with our method. A simple method for the production of nested sets might also lend itself to automation. This project will demonstrate this new method on a test gene and show that our method, in combination with our new vector, increases the efficiency of screening for deletions.